We give a simple probabilistic description of a transition between two states which leads to a generalized escort distribution. When the parameter of the distribution varies, it defines a parametric curve that we call an escort-path. The Rényi divergence appears as a natural by-product of the...

We present two extended forms of Fisher information that fit well in the context of nonextensive thermostatistics. We show that there exists an interplay between these generalized Fisher information, the generalized q-Gaussian distributions and the q-entropies. The minimum of the generalized...

In this paper, we present some geometric properties of the maximum entropy Tsallis-distributions under energy constraint. In the case q1, these distributions are proved to be marginals of uniform distributions on the sphere; in the case q1, they can be constructed as conditional distributions of...

We study H-theorems associated with the Brownian motion with constant drift on the hyperbolic plane. Since this random process satisfies a linear Fokker–Planck equation, it is easy to show that, up to a proper scaling, its Shannon entropy is increasing over time. As a consequence, its...

Quite general, analytical (both exact and approximate) forms for discrete probability distributions (PDs) that maximize Tsallis entropy for a fixed variance are here investigated. They apply, for instance, in a wide variety of scenarios in which the system is characterized by a series of...

In this paper we revisit the Bialynicki-Birula and Mycielski uncertainty principle and its cases of equality. This Shannon entropic version of the well-known Heisenberg uncertainty principle can be used when dealing with variables that admit no variance. In this paper, we extend this uncertainty...

We prove that the gravitational binding energy Ω of a self gravitating system described by a mass density distribution ρ(x) admits an upper bound B[ρ(x)] given by a simple function of an appropriate, non-additive Tsallis’ power-law entropic functional Sq evaluated on the density ρ. The...

q-Gaussian behavior is often encountered in quite distinct settings. A possible explanation is here given with reference to experimental scenarios in which data are gathered using a set-up that performs a normalization preprocessing. We show that the ensuing normalized input, as recorded by the...